While you can beat the story at level 55, you will notice a lot of the endgame content goes well above level 90, such as the Tainted Monsters #51-60 and the 10th Dreamer's Door Maze (which has a level 95 boss).
After completing the game 99% (all tainted monsters, side quests, and story chapters) you will just be level 75. That's still a long way from standing a chance against the toughest monsters.

The fastest leveling method is to repeat the final story boss.
He can be replayed unlimited times and gives half a level-up each try (takes roughly 5 minutes). To maximize the XP earned, put the Tactics Tweaker to favor XP, be sure to craft 3 x "Necklace of Enlightenment" at the Evermore Outfitter and equip it to your active characters. Also research everything at the Basic Training Ground & Officer's Training Ground. Lastly, assign 6 people to the Sage's Salon.

For the boss fight skip through all cutscenes, lock on to the boss with R3 and hit him with fast attacks (press Square-Button). You can even watch some TV or do other things along the way. Just press one button for a few minutes. Skip the cutscenes after the boss, save game, reload from main menu. Rinse and repeat.
It took me 6 hours getting from level 75 to 95 with this method. Then the 10th Maze got really easy. You can probably do it at level 85-90 but given that you must go through 30 floors again if you die, it's best to grind a few extra levels.